Related papers: Geometric Pattern Matching Reduces to k-SUM
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
Given a set of $n$ weighted points on the $x$-$y$ plane, we want to find a step function consisting of $k$ horizontal steps such that the maximum vertical weighted distance from any point to a step is minimized. We solve this problem in…
Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The…
This paper deals with the geometric multi-model fitting from noisy, unstructured point set data (e.g., laser scanned point clouds). We formulate multi-model fitting problem as a sequential decision making process. We then use a deep…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…
In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has…
In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied…
We consider the general problem of matching a subspace to a signal in R^N that has been observed indirectly (compressed) through a random projection. We are interested in the case where the collection of K-dimensional subspaces is…
We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…
For any given metric space, obtaining an offline optimal solution to the classical $k$-server problem can be reduced to solving a minimum-cost partial bipartite matching between two point sets $A$ and $B$ within that metric space. For…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
The classical pattern matching asks for locating all occurrences of one string, called the pattern, in another, called the text, where a string is simply a sequence of characters. Due to the potential practical applications, it is desirable…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their…
Direct sum theorems state that the cost of solving $k$ instances of a problem is at least $\Omega(k)$ times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a…
We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match…